(421e) Effective Generalized Disjunctive Programming (GDP) Models for Modular Plant Design
Evolving demands and increasing competition in the chemical processing industries drive a need for the most effective process design, at the right time. Engineers must identify the optimal configurations among many flowsheet alternatives in order to arrive at the desired design. One of the major approaches to synthesis is superstructure optimization, which involves postulating a superstructure representation of the alternatives, formulating a mathematical program to capture the decision logic, and applying a solution algorithm to determine the optimal configuration and operating conditions (Chen and Grossmann, 2017). Recently, there has been increased interest in modular designs due to their potential for improving safety, reliability, flexibility, and time-to-market (Baldea et al., 2017). While modularity on the product side has been addressed in depth (Rogers and Bottaci, 1997), new model extensions and methodologies for superstructure optimization must be developed to address modular process design challenges.
A hallmark of modular design is an emphasis shift from economies of scale towards economies of mass production, also referred to as ânumbering-upâ (Lier et al., 2015). This requires standardization of modules, a concept that has been explored in terms of aggregation of process units (Kampczyk et al., 2004) and cluster analysis to identify heat exchanger modules (Eilermann et al., 2017). This standardization implies that continuous design variables in the optimization formulation will now take values from some discrete set. While the introduction of discrete variables adds combinatorial complexity, it can also induce linearity in synthesis models, making them easier to solve (Voudouris and Grossmann, 1992).
In this work, motivated by Stephanopoulos and Westerberg (1980), we present a modification of the stage-wise heat exchanger network synthesis model from Yee and Grossmann (1990) that allows for incorporation of modular exchangers, selected from among a set of standard sizes. The modular design problem is formulated as a Generalized Disjunctive Programming (GDP) model Using this demonstration model, we show that discretization of the exchanger area allows for linear reformulations of the basic heat exchanger design equation, which is usually bilinear. Reformulation strengthens linear relaxations of the overall design problem, therefore aiding in the convergence of optimization solvers. Therefore, the consideration of modular process units and resulting discretization in design variables can even simplify solution of synthesis problems. We express the GDP model using the Pyomo optimization modeling library (Hart et al., 2017) in Python. Pyomo enables programmatic access to modify and manipulate modeling objects such as variables and constraints, allowing for automatic model interrogation and reformulation (Chen et al., 2018). Using Pyomo, we develop a plugin to automatically detect induced linearity from discrete modular design choices and reformulate the model to exploit the special structure.
Another central point of modular design is improved time-to-market due to expedited design, construction, commissioning, and startup of modular facilities. Several authors have examined the net present value (NPV) economic impact of switching to a modular design, including analysis on the sensitivity to the number of modules employed (Brodhagen et al., 2012; Lier and Grünewald, 2011; Mothes, 2015). We extend these studies using a model adapted from (Menezes et al., 2015) to examine the flowsheet design and construction scheduling of a process as a simultaneous GDP optimization problem, and demonstrate its value in balancing the trade-off between investment costs, operating costs, and time-to-market.
In this work, we demonstrate the value of effective GDP models both in capturing the logic and addressing the mathematics of modular chemical plant design. Through various case studies, we show how GDP enables investigation of key tenants of modular design.
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